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Homemean curvature (plane curve)

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# mean curvature (plane curve)

Let $\Gamma$ be a piecewise $C^{1}$ planar curve.

The *total curvature*, $\kappa_{{total}}$ , of $\Gamma$ is defined to be $\int_{{\Gamma}}|\kappa(s)|ds$ where $\Gamma$ is parameterized by arclength $s$
and $\kappa(s)$ is the curvature
of $\Gamma$.

The *mean curvature* of $\Gamma$ is defined to be the ratio of the total curvature to the length of $\Gamma$ :

$M(\Gamma)=\frac{\kappa_{{total}}(\Gamma)}{L(\Gamma)}$ |

Defines:

total curvature, mean curvature

Related:

MeanCurvatureAtSurfacePoint

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

53A04*no label found*

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